Abstract
In what is often called the “French didactical culture,” design has always played an essential role in research. This is attested by the introduction and institutionalization of a specific concept, that of didactical engineering, already in the early 1980s and by the way didactical engineering has accompanied the development of didactical research, both in its fundamental and applied dimensions. In this chapter, I present this vision of design and its characteristics as a research methodology, coming back to its historical origin in close connection with the development of the theory of didactical situations, tracing its evolution along the last three decades, and illustrating this methodology by some particular examples. I also consider current developments within this design culture, especially those linked to the integration of a design dimension into the anthropological theory of didactics and also to the idea of didactical engineering of second generation introduced for addressing more efficiently the development dimension of didactical engineering.
Keywords
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- 1.
In the theory, the milieu of a situation is defined as the system with which the student interacts, and which provides objective feedback to her. The milieu may comprise material and symbolic elements: artifacts, informative texts, data, results already obtained…, and also other students who collaborate or compete with the learner.
- 2.
The notion of epistemological obstacle, introduced by the philosopher Gaston Bachelard, was imported in the educational field by Guy Brousseau (1983) for expressing the fact that the development of mathematical knowledge necessarily faces obstacles, due to prior forms of knowledge that were relevant and successful in specific contexts. Epistemological obstacles are those attested in the historical development of knowledge, and having played a constitutive role in this development. Their identification may help understand students’ resistant errors and difficulties. Schneider (2014) provides a synthetic presentation and discussion of the notion, its development and use in mathematics education research.
- 3.
Among the many variables influencing the possible dynamics of a situation and its learning outcomes, didactical variables are those under the control of the teacher. In a situation of enlargement such as the well-known “Puzzle situation” by Brousseau, the number of pieces of the puzzle, their shapes and dimensions, the ratio of enlargement are didactical variables; the fact that students work in group, each student being asked to enlarge one piece of the puzzle is also a didactical variable.
- 4.
The notion of didactical contract is a fundamental notion in the theory of didactical situations (Brousseau 1997). It expresses the mutual expectations, partly explicit but mainly implicit, of students and teacher regarding the mathematical knowledge at stake in a given situation. The rules of the didactic contract often become visible when they are transgressed by one actor or another.
- 5.
The didactical and ludic contract is defined as the set of rules that, implicitly or explicitly, fixes the respective expectations and regulate the behaviour of one educator and one or several participants, in a project combining ludic and learning aims.
- 6.
COREM was the Center for observation and research in mathematics education created by Brousseau in Bordeaux in 1973. An experimental elementary school was attached to this center, with very advanced means for systematic data collection and storage. The data collected there during more than 20 years are still studied by researchers, for instance, in the frame of the national project VISA (http://visa.ens.lyon.fr). Detailed information is accessible at the following url: http://guy-brousseau.com/le-corem/acces-aux-documents-issus-des-observations-du-corem-1973-1999/
- 7.
This is the case for instance when pupils are asked to find a rational measure for a stick, a unit stick being provided, but the limitation of the physical space and material provided does not allow them to implement the strategy of commensuration.
- 8.
For instance, taking into account the fact that, in the neighbourhood of 0, the order of magnitude of x 2 + x is the order of magnitude of x.
- 9.
y3(x) = − x3 − 2 ∣ x ∣ + 4 at x = 0.
- 10.
y4(x) = 4 + sin(1/x)at x ≠ 0, = 4 at x = 0
- 11.
The notion of praxeology is central in the anthropological theory of didactics that considers that knowledge emerges from human practices and is shaped by the institutions where these practices develop. Praxeologies, which model human practices, at the most elemental level (punctual praxeologies), are defined as 4-uplets made of a type of task, a technique for solving this type of task, a discourse explaining and justifying the technique (technology), and a theory legitimating the technology itself.
- 12.
See the portal www.scientix.eu for information about these projects.
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Artigue, M. (2015). Perspectives on Design Research: The Case of Didactical Engineering. In: Bikner-Ahsbahs, A., Knipping, C., Presmeg, N. (eds) Approaches to Qualitative Research in Mathematics Education. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9181-6_17
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